1 Introduction to Nonequilibrium Statistical Physics and Its Foundations
7
Fig. 1.2 Small cube containing a certain amount of mass ρ where ρ is the mass density
and its sides. This amount changes because mass flows in and out of the volume
The net variation per unit time due to motion in the x direction is thus given by:
ρ v x
x
− ρ v x
x+
(1.3)
Analogously for directions y and z, one has:
ρ v y
y
− ρ v y
y+
(1.4)
ρ v z
z
− ρ v z
z+
(1.5)
The total content of mass in the volume is
ρ
(1.6)
so the variation in a time is
ρ
t+
− ρ
t
(1.7)
Then, the variation per unit time can be written as:
ρ
t+
− ρ
t
t
=
ρ v x
x
− ρ v x
x+
+
ρ v y
y
− ρ v y
y+
+
ρ v z
z
− ρ v z
z+
(1.8)
Divide by